Twin peaks in rf spectra of Fermi gases at unitarity

We calculate the radio-frequency spectrum of balanced and imbalanced ultracold Fermi gases in the normal phase at unitarity. For the homogeneous case the spectrum of both the majority and minority components always has a single peak even in the pseudogap regime. We furthermore show how the double-peak structures observed in recent experiments arise due to the inhomogeneity of the trapped gas. The main experimental features observed above the critical temperature in the recent experiment of Schunck et al. [Science 316, 867 (2007)] are recovered with no fitting parameters.

Figure 1

(a) The atomic propagator for the $\mid 2⟩$ atoms: thin (thick) lines are noninteracting (interacting) Green’s functions, $\Sigma$ is the self-energy, and $\Gamma$ is the $T$ matrix treating the interaction with the $\mid 1⟩$ atoms in the ladder approximation. (b) The correlation function $\mathcal{D}$.

Figure 2

(Color online) Radio-frequency spectrum of a homogeneous Fermi gas with equal populations. Inset: Spectral function for a balanced system at $T=0.3T_F$ and for the minority component of an imbalanced system at $T=0.05T_F$ $(k_{\mu }=\sqrt{2m\mu })$.

Figure 3

(Color online) Radio-frequency spectrum of the majority and minority components (respectively, in the main figure and in the inset) of a homogeneous gas for various imbalances $\sigma =(n_1-n_2)∕(n_1+n_2)$ at $T=0.3T_F$ and constant $n_1$.

Figure 4

(Color online) Radio-frequency spectrum of the minority component of a trapped Fermi gas with population imbalance $\delta =0.9$. Each spectrum satisfies the sum rule, Eq. (4), but here curves are normalized such that they reach 1 at their highest peak.

Figure 5

(Color online) Surface plot of the integrand $r^2\mathrm{Im}\mathcal{D}(r,\omega )$ of the trapping average at $\delta =0.9$ and $T=0.4T_F$ for the minority component. In the inset, we plot $n_1\left(r\right)∕n_1\left(0\right)$ (dashed line), $n_2\left(r\right)∕n_1\left(0\right)$ (continuous line), and $r^2{n}_2\left(r\right)∕R_{TF}^2{n}_2\left(0\right)$ (dot-dashed line).